Going renewable (part 2)

In my previous post I discussed what it would take for me to harvest the entirety of my family's energy usage on our own property using renewable sources. This resulted in the determination that I'd need to install 9,400 square feet of solar collectors at an approximate cost of $900,000. Clearly, this isn't a practical calculation for an actual plan. Nor was it meant to imply that photovoltaics are impractical or a waste. Rather, the point was that for the U.S. as a whole to be free of the need for fossil fuel, it will take more than panels on rooftops.



A reader (Mark) was kind enough to leave a comment. His point was that I'm being misleading in producing such figures. He also pointed out that using solar power in a grid connected system to produce more electrical energy than is used by a homeowner is a waste, at least in a financial sense, because the utility purchases such excess power at wholesale rates (tied to what they pay per kilowatt hour from their normal sources). Up to that point, they effectively pay the homeowner retail, since they utilize so-called "net metering" and when the system is producing more power than is being used, the meter literally spins backward.



In order to determine the figures for what I'd need to net out our household electrical use, I can use the figures from the post referred to above and my post on my family's total energy use. Using this data, I'd need 660 square feet of collector area (say 22' X 30') to supply a system capable of delivering about 8 kilowatts for about $64,000. Much more realistic, but I better goose it up a little bit because we're now talking about "practical" systems, and such systems don't convert sunlight at 20% efficiency today. Let's say a 10 kilowatt system for $80,000. Tax credits and other government inducements might cut this cost in half. So I could, in theory, free myself from paying for electricity by spending $40,000. Obviously, every single thing I can do to reduce energy usage will pay off massively.



Now, let's dig into the figures from part 1 a little more deeply. In my post totaling my family's energy use, I determined that we currently spend something like $35,000 per year on total energy costs. To offset that, I'd need to spend $900,000. Let's ignore maintenance costs and figure that a $900,000 investment would return $35,000/year for a system life span of 20 years. Finally, let's assume that my cost of capital is about 6.5%, about the going rate for a second trust deed (not that I have $900,000 in equity). So what's the net present value of using $900,000 at 6.5% interest to generate an income of $35,000/year? Clearly it's going to be negative since 20 times $35,000 is only $700,000. Thus, at current energy prices, it doesn't pay to go totally renewable, even if it were possible to do so.



Finally, let's figure what energy would have to cost in order for an investment of $900,000 to pay a reasonable rate of return. Let's call that rate 10.5%, that's a break even return on money that costs 6.5% with inflation at 4%. And we'll assume a lifespan of 20 years. The investment would have to return about $109,000/year. That implies that the cost of energy would have to increase by $109,000/$35,000 or a little over three times to make it "calc out." With the government offering to pay half my costs (sort of) it might only have to increase by 50%.



Of course, all of these figures are theoretical because my energy figures incorporate embedded energy in food and goods, all transportation costs, etc. And the $35,000 per year includes gasoline, coal burned and uranium decayed to make electricity for the house and factories, etc. all accounted for at a single rate of probably questionable accuracy. Nevertheless, the ratios are approximately correct, so the implied price increases of energy (or, inversely, the implied decrease in the cost of renewables) should be about right. It won't be long, since both numbers are heading quickly in the "right" direction.

Going renewable (part 1)

My last couple of posts have dealt with my family's overall use of energy. I've calculated it in terms of equivalent continuous power and included transportation, food, durable and consumer goods, and household energy use. For those unclear on the distinction between power and energy, an analogy would be that power in watts (and kilowatts, etc.) is to speed in miles per hour as energy in kilowatt hours (or, equivalently, 3,600,000 joules) is to distance in miles. Or, alternatively, power is to energy as speed is to distance. You can go a long way by going fast for a little while or going slowly for a long time. Equivalently, you can use a lot of energy by using a lot of power (watts) for a short time or a little power for a long time. So my calculation of our family's use of energy at the rate of around 40 kilowatts is the average "speed" of constant rate energy use that would use the same amount of energy at the end of, say, a month that our actual sporadic use totals.



In thinking about what it would take to go completely renewable, several factors must be considered. First is that I don't really need to be able to supply power at the rate of 40 kilowatts. A lot of the energy conversion in that number is from the consumption of food and consumer goods. However, if I'm really intending to be entirely sustainable, I should put energy into the grid to compensate for that used in those types of consumption. The same rationale applies to transportation fuel. For this reason, I'll proceed as if that's what I'm going to do.



Next, what renewable sources are available to me? Such exotics as geothermal and tidal are not scaleable to my needs, even if they were geographically and geologically available. Wind is not practical because wind of sufficient velocity is infrequent and the (%$#&*&^%) homeowners' association would never let me put in a tower. (Note to self: NEVER buy a house where there's a homeowners' association). So solar seems to be my only "realistic" option. The reason for the quotation marks will become clear later.



So, should it be photovoltaics? How about a concentrator heating a liquid to boil water and run a turbine? Passive solar for water and home heating? All of the above? Well, what can the sun deliver to me? I'm in Southern California at a latitude of about 33 degrees 50 minutes. Using the U.S. Solar Radiation Resource Map from the National Renewable Energy Laboratory I find that with a two-axis tracking flat plate collector during the worst months of the year I should be able to collect, on average, about 5.5 kilowatt hours/square meter/day of solar energy.



Suppose that I can use, in some fashion, this insolation with 20% efficiency (difficult on my scale but certainly possible on an industrial scale). I'd have 1.1 kilowatt hour/square meter/day available to me. Now our 40 kilowatt rate of consumption is equivalent to 960 kilowatt hours/day, so I'll need to collect solar radiation at 20% efficiency over an area of 960/1.1=873 square meters. Hmmm... That's about 9400 square feet, or an area 94 feet wide by 100 feet long. Our south-facing roof is not that big. Our whole two story house's floor area is only 2480 square feet. I do think that our lot is big enough to encompass such an area of 0.22 acres, but not by much. OK, so I'll erect a structure that spans corner to corner both ways on our lot and top it with some as yet to be determined type of collector.



Now that my needs are defined, what about the type of system and the cost? This is a complex area in which I am by no means an expert. But that has never stopped me before, so let's give it a go. I speculate that setting up a solar to steam turbine system in my suburban neighborhood that can deliver the kind of power I'm discussing here won't be permitted so it appears that photovoltaics is my only option (note that I've dropped the "realistic"). It's impossible that I could cover my lot with photovoltaic panels, so I'd have to use the strategy of concentrating the energy. Maybe mylar sun-tracking reflectors to concentrate the incoming solar energy onto a much smaller set of panels.



Now in June at local noon, I might expect something like 1,300 watts/meter^2 over my 873 meter^2 or a capacity for output of about 227 kilowatts at 20% efficiency. So at an installed rate on the order of $8,000 per kilowatt, I'm looking at spending about $1,800,000. This overstates the requirement by a little bit, since I've sized my system to supply the energy we use in the short, low-sun days of December and January. So I'll cut this in half, to $900,000. I wonder if they take VISA?



Obviously, before getting out the plastic or taking out a second on the house, etc. the most economical thing by far is to reduce consumption. This is easy to say and, in my experience, difficult to do. Compact fluorescent bulbs, turning off lights in rooms not being used, reducing the amount of time the pool filter runs, etc., only nibble at the margins. The biggest consumer is my wife's use of automobile fuel, the next two largest are her and the children's "stuff" consumption and my automobile fuel. Dramatically reducing these would be a huge lifestyle change. But it's going to have to be done.



As discouraging as this is, there's a positive element to it. My family is a fairly hefty consumer of energy, and yet the sun provides enough energy to supply us with our needs over the area of the property we own. If we extrapolate that nationwide, the possibility exists that we could actually become self-sufficient and sustainable. There are many, MANY, MANY hurdles to be overcome but there's reason to think it just might not be impossible. It's now up to us to figure out how to make it happen.

Carbon footprint adventures

I made some calculations in my last post regarding my family's use of fossil fuels. I attempted to determine as complete a picture as I could, including such things as goods consumption, food, etc. I also utilized a very simplistic model, assuming all our fossil fuel consumption could be modeled by the chemical combination of n-heptane with atmospheric oxygen to produce carbon dioxide and water to estimate our production of carbon dioxide as a result of our energy use. While this undoubtedly leads to inaccuracies, I think it is "in the ballpark."



Since publishing that post, I've played a little bit with the so-called "carbon footprint calculators" to be found all over the web. I've also been as thorough with them as I know how and as they will allow. The results are rather disturbing, if one buys into the theory of anthropogenic global warming by way of carbon dioxide emissions. My "ground up" calculations indicated that my family produces 96 tons per year of carbon dioxide emissions, whereas the calculator linked above shows about 44 tons. This is a rather significant under estimation by more than half, if my calculations are correct. And though they may be off, I don't believe that they are off by that amount.



Now I suppose that those who model climate do so using a better estimate of carbon dioxide emissions than a summation of everyone's output from the carbon footprint calculator. Nevertheless, I imagine many people log on to such sites to determine their footprint and what they can do about it. Based on my results, they severely underestimate the extent of the emissions for which they are responsible and the remedial measures they would need to take.



Assuming that the averages shown on the calculator site are off by the same extent as the results of my calculations, my family of four emits carbon dioxide at a rate of about double the national average, a little under four times the average for so-called "industrial countries," about ten times the world average, and about twenty times the worldwide goal. That is, my family would have to reduce its emissions by about 95% to bring us into accord with that goal.



Wow. If both my wife and I stopped driving, and I stopped flying my airplane, we'd reduce our footprint by just over 50%. In fact, our food consumption alone represents over 8% of our carbon footprint, and thus we would have to eliminate all carbon emissions not involving eating and change our eating to less carbon intensive sources to reduce our footprint by 95%. And as I pointed out in the previous post, this does not take into account our pro-rata share of institutional use of fossil fuels such as military, etc.



If this is truly an accurate representation of our situation and only differs from others in the United States by degree but not basic nature, we aren't going to be able to meet such goals no matter how many conferences in Bali are flown to by worldwide climate diplomats. So what then?



After calculating our footprint, we're given the option of "offsetting" all or part of our carbon dioxide emissions. What would I have to do? I'm given three options: contributing $598 to a "Clean Energy Fund;" contributing $777 to Reforestation in Kenya; and contributing $1,304 to "UK Tree Planting." I get a certificate and everything. Keep in mind, however, that these amounts reflect the carbon dioxide calculated by the calculator at the site, not the ones I calculated from scratch. Those would require over double the expenditure. I guess this is how Al Gore flies around the world and lives in a mansion and yet has a positive effect on climate change. Somehow, I don't feel that everyone buying these offsets will solve our problems.

Total energy use in my family

In an earlier post I utilized data in the World Almanac and Book of Facts to determine that the total per capita rate of energy consumption in the United States is a little over 11,000 watts. I decided to see where my family and I fall into this. I approximated all of the electrical consumers in the house, the fuel consumption of my vehicle, my wife's vehicle, my airplane, the power I use at work, the power she uses at work, the energy content of the food each of us eats, and the energy content of the items each of us "consumes."



Obviously, many approximations and estimations were necessary but the results are quite interesting to me. It appears that my family of four consumes energy at the rate of about 40,094 watts. This is all-inclusive as best I can make it, but does not include our pro-rata share of government expenditures (this could be significant, considering it would include our share of military expenditures of energy, etc.). Surprisingly, this amounts to 10,023 watts per capita in my family. I find this agreement with the figures from the Almanac to be downright startling and, frankly, quite gratifying. It's a little misleading though, since the Almanac figures are the total of U.S. energy use whereas, as we'll see later, a significant portion of my family's energy consumption likely takes place offshore.



The largest single item is my wife's use of automobile gasoline in her Grand Cherokee Laredo. This came to 11,880 watts. She uses a LOT of gas.The next is her consumption of "stuff." I don't know exactly what she buys, so I used the the money she spends as a proxy. I excluded food, since it's included separately, then figured one third the cost represents energy input. In earlier days it would have been less, since there would be more input of labor but in this automated day and age, I figure one third. Then I estimated the cost of a joule of energy (about $2.778*10^-8) and worked back to rate of consumption normalized to represent continuous consumption. Since the two children that share our house are hers, I lumped all consumption that is not mine into hers. The total for this category is 10,400 watts. This is the where the "offshore" portion mentioned above comes in, since a significant portion of the energy input for our "stuff" purchases is in places like China.



Next came my use of automobile gasoline at 5,049 watts, followed by aviation gas for my airplane at 3,961 watts. The house consumes energy at the rate of about 2,812 watts. I used a separate spreadsheet to go item by item in the house, the largest consumer on the continuous, annualized basis is the refrigerator, followed by the swimming pool pump. My goods consumption comes in at 2,400 watts. Total food for the four of us is 3,294 watts. Amazingly, taking my house completely "off the grid" would only reduce our family's total fossil fuel energy expenditure by about 7%. As an aside, I should point out that I'm carrying many more digits of accuracy than my approximations justify, the best of them are probably good for two significant figures.



From a carbon footprint point of view, I assume that 100% of our energy use comes from burning fossil fuels, and that 6 pounds of fossil fuel provides 125,000,000 joules of energy and produces 19 pounds of carbon dioxide. That means that our rate of energy consumption results in the annual addition to the atmosphere of 96 tons of carbon dioxide. From an economic point of view, my family spends something like $35,000 per year on energy.



I mentioned in my article about the Almanac that I was confident I could reduce my rate of energy consumption by half. I'm less confident now that it would be relatively easy, but circumstances will surely force us to do this and much more. At least I now know where to start looking for the savings.